Power of a Matrix

A = {[2 1 2 ] [2 1 2 ] [2 1 2 ]}^8
Compute the power matrix using the PDP^-1
I got the eigen values to be 1, 2.
i am having difficulty forming the vector and therefore continuing the question. Could anyone explain this?

A = {[2 1 2 ] [2 1 2 ] [2 1 2 ]}^8
Compute the power matrix using the PDP^-1
I got the eigen values to be 1, 2.
i am having difficulty forming the vector and therefore continuing the question. Could anyone explain this?

Is that meant to mean that the three rows of A are all equal to 1 2 1? If so, the eigenvalues are 0 and 5, not 1 and 2. Please supply a correct version of the problem.

Have you tried multiplying the matrix by itself to see what its square looks like? If so, did you notice that the square is exactly 5 times the original matrix? So what would happen if you squared the result again? And again?